Speaking to hundreds of members of the Catholic Church, including senior clergy, the Pope said he was gravely concerned by "the immense suffering" caused by the abuse, especially by Church ministers.

He also acknowledged "the shame and humiliation" caused by "these sins".

"Above all, I express my deep sorrow to the innocent victims of these unspeakable crimes, along with my hope that the power of Christ's grace, his sacrifice of reconciliation, will bring deep healing and peace to their lives," he told the congregation.

He said he hoped this "chastisement will contribute to the healing of the victims, the purification of the Church and the renewal of her age-old commitment to the education and care of young people".

"I express my gratitude for the efforts being made to address this problem responsibly, and I ask all of you to show your concern for the victims and solidarity with your priests."

Analysis

By James RobbinsDiplomatic correspondent

This is Pope Benedict's most outspoken apology on this visit so far. He expressed deep sorrow to the innocent victims of what he called these "unspeakable crimes".

But the Pope also accepted that the Catholic Church as a whole had failed when he spoke of the "shame and humiliation all of us have suffered".

That will be seen by many as coming close to the equivalent of an admission of corporate guilt, but still Pope Benedict made no mention in his address of the systematic cover-up by the Catholic Church over many years of abuse around the world.

So, although this latest apology will satisfy many within the Church and also some of its critics outside the faith, it may not be enough to satisfy some of the victims and those campaigning on their behalf.

Later it was confirmed that the Pope had held a private 30-minute meeting at the Vatican ambassador's home in Wimbledon with five abuse survivors, three of whom were from Yorkshire, one from London and another from Scotland.

The Vatican said during the intensely emotional meeting, which began and ended with prayers, the Pope expressed his "deep sorrow and shame" to the four women and one man.

Bill Kilgallon, chairman of the National Catholic Safeguarding Commission, said he spoke to the abuse survivors beforehand and they were "understandably quite emotional".

"I would not say they were angry but I think there's anger in them," he said.

"I think that's a really positive thing because what happened was a real betrayal of trust."

Later, representatives from the safeguarding commission, including Mr Kilgallon, met the Pope in a separate meeting in Vauxhall.

Commenting on the Pope's message during the Westminster Mass, Peter Isely, of the Survivors Network of those Abused by Priests, said: "We don't need a Pope who is sad about crimes. We need a Pope who will prevent crimes. And his words prevent nothing."

Peter Saunders, chief executive of the National Association for People Abused in Childhood, who was also a victim himself, called on the Pope to make funding available to abuse survivors and provide access to Vatican files.

During the afternoon a march and rally organised by Protest the Pope - an umbrella campaign group opposed to the Pope's visit - took place in central London.

Crowds lined the streets on the route to Hyde Park to catch a glimpse of the Pope or even a kiss

Organisers said 20,000 people took part but the police said they were unable to confirm numbers.

Gay rights campaigner Peter Tatchell, who was on the march, said if he had the chance to speak to the Pope, he would ask him to hand over any secret Vatican sex abuse files and co-operate with the police.

"The Pope keeps apologising but he only apologises for the failings of others. He is not a person who deserves the honour of a state visit," he said.

In the evening, tens of thousands of people took part in an open-air prayer vigil in London's Hyde Park.

As darkness fell, pilgrims waved Papal standards and candles as the Pope read prayers from a vast stage surrounded by choirs and clergy.

Teenage Britain's Got Talent singer Liam McNally performed a solo before the Pope departed to much applause.

Earlier engagements included a meeting with Prime Minister David Cameron, his deputy Nick Clegg and acting Labour leader Harriet Harman. The former prime minister Tony Blair, a convert to Catholicism, attended the Mass at Westminster.

There were also opportunities for the Pope to meet the public, including the young and old.

Thousands of young Catholics greeted him to cheers outside the cathedral. Among them was Paschal Uche, 21, who told the Pope: "Your visit brings us together. It is like a family reunion and we are very, very pleased to see you."

At the scene

By John Hand, BBC News, at Hyde Park vigil

First came the hours of build-up, with singers, dancers and Carol Vorderman entertaining a crowd swelling towards 80,000 in a festival-like atmosphere. The paths dissecting Hyde Park became a river of people proudly parading school banners, national flags and the odd crafty pint of something alcoholic (that wasn't communion wine).

The excitement grew further as the Pope approached Hyde Park, with an animated group of pupils from Chelmsford's St John Payne School playing "spot-the-Popemobile" until 11-year-old Katie Keown shrieked "I see it, it's here!" to end their six-hour wait for the star of the show.

But after the last couple of days of pomp and ceremony, this evening was another side of the Catholic Church - a prayer vigil reverently observed by a gathering of many ages, many nationalities but one shared faith. As evening fell, imitation candles were retrieved from handbags and, when Pope Benedict spoke, there was complete silence from the crowd-turned-congregation which clearly wanted to hear and understand every word uttered.

Afterwards, many streamed away in quiet contemplation. So, not your typical Saturday night out in central London. But then again, not your typical headline act.

Later he visited St Peter's Residence for Older People in Vauxhall, south London, where the 83-year-old said he had experienced the "joys and the struggles" of age.

"The provision of care for the elderly should be considered not so much as an act of generosity as the repayment of a debt of gratitude," he said.

The Pope added that the growing number of old people was a "blessing" for society and that every generation could learn from the experience and wisdom of the generation that preceded it.

The day also saw the Pope speak of his "deep love" for the Welsh people and deliver a blessing to the nation in Welsh.

The Pope's schedule is continuing as planned, despite six men being held in connection with an alleged terrorist threat to his visit. Sources at Scotland Yard told the BBC that detectives have interviewed the men and believe there was "no credible threat" to the Pope.

The street cleaners for Veolia Environment Services, a cleaning company working for Westminster Council, were arrested on Friday after being overheard in the works canteen apparently plotting an attack.

Police have refused to confirm reports that they were joking, and say they had to investigate what might have been a genuine threat.

The men can be held until early on Sunday before police must apply for an extension.

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